Incremental costing is the basis for dispatch of multiple generating units in electric power generation systems. The incremental cost is the product of the incremental heat rate (IHR) and fuel cost. Some companies also include incremental maintenance, and other operating costs that are directly attributable to production, in the incremental cost calculation. To optimize economies, all generating units supplying a common load should operate at the same incremental cost, as shown in FIG. 1. As is known in the art, FIG. 1 plots Incremental Cost, in dollars per megawatt-hour ($/MWhr), against Unit Output, in megawatts (MW), for two discrete units, Unit A and Unit B. Specifically, FIG. 1 shows the unit loading required to deliver 807 MW from the two-unit system, where the incremental cost, or lambda (λ), is 30.41 $/MWhr. As system load changes, the incremental cost, or system lambda, increases or decreases until the sum of the unit loads matches the system load demand. Each unit is also constrained by its minimum stable load and maximum capacity.
In the industry, incremental heat rate curves are usually developed from periodic performance tests. As is known in the art, an Input/Output (I/O) curve, shown in FIG. 2, represents the total heat input to a power generating unit as a function of the gross output (the total power generated by the unit) or net output (gross output less the power used by the unit's pumps, fans and other internal equipment). FIG. 2 shows Heat Input, in BTU/hour, vs. Unit Output, in megawatts, and further shows the minimum and maximum capacity of Unit A and Unit B. These data are fit to a polynomial curve, typically of the third to sixth order, which commonly has a defined constraint of being monotonically increasing within the unit's operating range or minimum to maximum capacity. As is known in the art, the unit heat rate, shown in FIG. 3, is heat input divided by unit output, and represents the unit's overall performance. Incremental heat rate is the first mathematical derivative of the I/O curve, or d(I/O)/d(MW). All three curves—input/output, heat rate and incremental heat rate—can be presented as gross or net, depending on the operating and dispatch philosophies of the company.
Performance tests are usually run under carefully controlled conditions to form a baseline or nominal Input/Output curve. The most common controlled conditions are main steam pressure, main steam temperature and hot reheat temperature. Other parameters may not be controllable, but are corrected in the unit performance calculations to standard conditions, typically design or achievable values for the generating unit. Such parameters include steam reheater pressure drop, condenser pressure or circulating water temperature, ambient air temperature and barometric pressure. Valve lineups or generating unit configuration can also change either for operating load or for maintenance. Fuel makeup, or ultimate analysis, is important, but usually not an adjustment factor in the calculations.
Currently, in the industry, the performance curves are updated only occasionally, perhaps annually, but often less frequently. However, between the updates, variations in any of the baseline conditions or lineups may cause changes in the unit's performance and capacity. When adjustments are made to unit performance for these variations, the adjustment typically amounts to the application of a few standard correction curves, or factors from these curves, which are typically supplied by the equipment vendors for design operation of a new unit. Considering the normal variations in steam temperatures and pressures, several or many operating parameters can be off-nominal at any moment, so the IHR can regularly be 1-5% in error, resulting in 0.5 to 2% inefficiency in the overall system dispatch.
Therefore, there is a need in the art for methods and systems for calculating and predicting performance in near real-time, to optimize generation costing. In addition, as public concern about emissions, and the resulting legislation, continue to evolve, there is also a need in the art to track and predict emissions from generating units and to quantify their production rates and cumulative quantities.